What would be the appearance of the Moon if it mvp /wlt4dr 1*3 ge3xrhad
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet iq;m u5oa6;kz fn the harbor of Syracuse by focusing the razq6;u ; komf5ays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirwl 4/tn8 j8tu nl-j6voror appears to reverse left and right, it doesn’t reverse up and dlt voj/ 6 t8-n84njwluown. Explain.

If a concave mirror produces a real imagen:fv vv mn:5 b)nzwd7+, is the image necessarily inverted? Expla):vbwv dz7nn:5v +fmnin.

An object is placed along the principal axis of a sphericaooc+sz)p-h: 2r ej+ evl mirror. The magnification of the object is -3.0 Is the image real or v z2sp)+-hce +oo:evjrirtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussedt hu) oeppzbx:9 lb f1*2vu0fv(b/tx5 with reference to (Fig. Below a), drvt bux10e ) p*zb po b/(:fu9fl5t2xvhaw ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? Wha./pf mhkm5o cche/ ptcppbaq5c(; :2 *ey8xf0 t is the magnification of a plane h mx55 /.b/ep qh;*:20 fcty8ca(pfppem occkmirror?

When you look at the Moon’s reflection from a i; f4bi04 odq(ra7y bdripply sea, it appears elongated . Explad f ;qydb7(440irba oiin.

What is the angle of refraction when a light ray meets the boundar rmcss+m5 vd)c y(wzc7+d; x( xai0om5y between two mate csm)c5xrsmo++mxy diz (wvdca(057; rials perpendicularly?

How might you determine the speed of light in a solid, rectangular, transparent 1 ma+ /phy0hei6f;kpq objea1py6hh; +0/ mpi kfqect?

When you look down into 6il6wtq b:81m o)y aula swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent y68tqli6owumb:)l1 a depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is un4be )iyrz-*e hq r5,tnp8xa:g/ xoh/hder water 8gh/b 4,z er/r-xneo*tph qax) i5yh:(Fig. Below).

Your eye looks into an aquarium and views a fish inside. One ray of light that e2;n48xu whn:l6e3 n m4nedbhrmerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Brief3wnuen h:nxd n2m8erl;44bh 6ly justify your answer.

How can you “see” a round drop of wazmcjxh+))pgi e-+:zv j e7el1 ter on a table even though the water is transparent and colorless?j:ljp-ehzc+ g1 7v+)zxie me)

When you look up at an object in air from beneath the surfa8*ad;r1r kovsh 0l v*yce in a swimming pool, does the object a oryslk* v10r hdav8;*ppear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a ne 06ibbjev mgt ;cq;/4ke0vd-lgative object distance?

Light rays from stars (including our Sun) always bend towary,:ae pl0f + tu,(:m,j zygwzkqu6a*wd the vertical direction as they pass through the Earth’s atmoamw : pq+ a:0z(ezflkwgj,6,tu *uyy,sphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed iy;;l3beihvbt4bh 52 +/2b ufqh dudp+gav67a f a camera lens is to make a sharp image of an object very far awai dbqe/bl2523bt;g a6bh h vu+hpyf7;duav+4 y?

What type of mirror is shown in pif+ 6kbk7 qot0q/+ox (Fig. Below)? Explain.

A photographer moves closer to his subject anf5 w; /dzmz9ufya5b 8sy1(opy d then refocuses. Does the camera lens move fartu;wbf/szz y8p55d9yf oy (1ma her from or closer to the film? Explain.

Can a diverging lens form a real image f-vz5s;qlmi9s aga8 t40 /:snvre 5nzunder any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is s/kh(xs+r9y vs/ow6b,5s ez c53tdgialways inverted, whereas a virtual image is a(czyssh5g+x5 b sr/d3s6eowi/k 9 ,t vlways upright if the object is real.

Light rays are said to be “reversible.” Is this consistent wp*4-. r*lt7af-pkiabawzmm5 ith the thin lens equation? Erw aa 5f-k*p4p -7mblmiz*t. axplain.

Can real images be projected on a screen? Can virtual images? :(apo;x.s,pz n 0amek Can either be photographed? Discx ap, s0:pmke;no(.azuss carefully.

A thin converging lens is moved closer to a nearby object. Do40fm)lkoi0 5 6x xfkgoes the real image formed changlfg450x60ko ox )if kme
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30+f8efpk2 rbfh:e- -w i In air, it is a converging lens. Will it still be a converging lens if plp8f i:hk-fe+ -wr2 fbeaced in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a conavao3jc b p79gi1 nzjva9;y/ (verging lens. If the nose and the tail ar/zp ;an7c (aa9ojgv9 y 31ibvje each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands faci, f4ig,ftr5 nnm07oping a converging lens. Under what circumstances (if any) would the image of the nose be if,f,ior74pmg nn t05 virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging l.q1z2p9iwaihg1c2v a ens have a shorter focal length than the diverging lens if the latter’s foc1zqpaw 9v12gi.aic h2al length is to be determined by combining them?

Explain how you could have a virtual object.f, 4z+h qz caqhs16bgle k1nr2cc7i: 2

  An unsymmetrical lens (say,7zzqycfc-v c3s5i 2 y7 planoconvex) forms an image of a nearby object. Does the image point change if the lens is turncqcz23vys z 77 yci5f-ed around? ----待选择----yesno 

The thicker a double convex lp2 5if6hcnku:ens is in the center as compared to its edges, the shorter its focal lenich5u k2:6pf ngth for a given lens diameter. Explain.

Consider two converging lenses separated by some d332t0 rp ggz vp /m5b0pb 5dlxk91nwdristance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an i 3 g5d m rbzgdbpk00p23nprwtl1/vx95mage? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at y mr0xqyqc,h4+ our image in a flat mirror 2.5 m away. For what distance should the camera len0h cxr+y4m, qqs be focused?    m

When you look at yourself in a 60-cw3qp;(n:gz endf,49jjc+ e hcm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be tj+ hfz( ;cnjqc n9:ge4dwe,3prue.

  Two mirrors meet at a 13ajep32qk5,e3dh /q f8vluqxy9+gmc) 5$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floook,kyyhi5 ju((2 vd9ucm0hm3 r stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be k(yhh2,0y3(oi vm9 mcdkj uu5seen reflected in the mirror?    cm

  Suppose you are 90 cm frhx,e ( tzim5 8fv2gusa42 q(ohom a plane mirror. What area of the mirror is used to reflect the e, txiq4a2zhv(sf8m uh2g5 (o rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an ang dtml lar6oaw3rl b0g:2/rv2 4le $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, fox4zc: /u/juz m/nlbz2cuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which xmbzln j 42c//uz/u z:the mirror was made?    cm

  How far from a concave mirror (radius 23.0r 4ihgk hp/n*1)dr5sth f6l -n cm) must an object be placed if its image is to bfs *rikh )t1n56 d-rg/p4hnhle at infinity?    cm

  If you look at yourself in a shiny Christmas t .qsymoq ;/d: j i8,ui)rn.zvaree ball with a diameter of 9.0 cm when yj/)mi rs ,o.iavqn q.:uz8d;your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park sho768p gjzakl1 wl3a) a eha.w9kws an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature? p1hkae9gwwaa7)6ll .a k38jz   cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, wk c: dyu7sq*sah5b41mill produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you tha ba9 ruhvyc(t0b6ty;.t are smaller than they would be if the mirror were flat. Are the mirrors con9h; (ab v0.yt yruc6btcave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is ptc nw7*nnt.k2 laced 20.0 cm from a convex mirror of radius of ctn* k.wc 2n7tnurvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. You9nw:d r6d,qrtoy56dc,d oz2v estimate the heivdd,odwz5 2r96tnyqr :,6doc ght of your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so th-tt5 fy7wi+iga j(kc:at it produces an image (f: i7ck5g-itywtja+at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is tsb9;9hn l /uj( e6svg*btj (fvirtual and very small when viewed in a curved mirror. The image app*svj6beul( /n bgt9(j;9 s htfears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniquqemuk6v.:2bhfzbo74 ; y apz+es,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mirror :rg9;w/d ld s3sk 34 ltanv-jlr2w:btis $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equatjpeq (4xz:v l8hn8 d.lion, Eq. 23–2, is valid for a convex mirror as long as f is considerel(4p.:qx8v e8lh ndjzd negative.

  The magnification of a conl qno/7c*bp:vl4migxi2vx2n+ 6pnq nwq)d 8)vex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 c,).:x2n lwwxizjs j8pm in front of a spherical mirror. It is desired to produce a vip2w ,zs.j8:lx)jxnw irtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 whs jyl3m9fk c61en 1s3ck9m 6l fyjyour face is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in 0o. o ahh6oumb9lt6e )
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice is4mt df4fz s bw((ozok b*. heu8z1ceu )y6c;z* $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in atk h4vj;;.mhv vv:cf5v 4chb,is)x c9 certain substance is 89% of its value in water. What is the index of refraction of this substancechv 5 bv9vt4ih kx),.fmchjvs ;:v 4c;? n =   

  A flashlight beam strikes the surface of a plj4a )xn)rlais )u/ey-dfh;ez -3 * pjane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from be7uev9ubz. e. eneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at an an8.g0mz dxvm9 urr,l di-pk8. lgle of 66vr88m,l dd.-pm9l k0xriguz ..0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to makelfx le bf8+c, + ov7p)0j+e ea7qj5ldr a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of refractio89( jzxhy5unai.i ve0-kf s h:n is 1.52. A beam of light from outside 8k.-9 u :ahyixjvi5( f0 senhzthe aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool crosj4q. 94l.k a 9cauat night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the s r99.cuaaq44.lc ko jspot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prismkqs. fd)nz r+:w jp 7bo4r(l;y at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air st ii :kxi-:bl,trikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of ref-,lb:xi i: kitraction.    $^{\circ}\,$

Prove in general that for a7ex./rpr3b zx light beam incident on a uniform layer of transparent material, as7 .xrx 3brpze/ in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident :8tr a0bm+ u1oqgx*b;w malr ;on a flat piece of glass with index of refraction n as in (Fig. Below). Show that if the inci1ba:g lx*m mubr;+twq 0ra ;8odent angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between wate1ax -d 7ryp usk.os3lm.f6dx/ r and Lucite? To be totally internally refds pxr.am 6d-o/1ls yfx7ku3 .lected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air sur)t4jylhy (6 1t 9lsvasface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of waxg ln/y; (*,u+mr jjvmf6m1 lgter from a depth of 62.0 cm. Where must it strike the air,gnrujvj 1ml gm x f6+*(y/;ml–water interface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the s l1f/7ytc(/vj0ccc 3 y6.+igrburwxiurface of a liquid and strikes the surface 7.0 cm 03cig wr6 c+xy1lj c(ri/ vctu7y./ bffrom the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in6 xfl9 se 12(a8y h5/iwzkvpdg jdcgfyh)92r4 (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as shown b38 qz2rw a0llin (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about b 0rz 3wql28la1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index5b2 v oea(x69z3xshro of refraction for a glass or plastic prism to be used in binocula6ho x v9xba3zs5or2e( rs (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 6ef82ti pkp.mu3.(7it r for j;5.0-mm-focal-length converging lens. Find the objectukjm .fo ttrpi3fi(.7 2 pre8; distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.o 7o45g)zi)) mp 9/gxt5 m1bdwimnyat 5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an imas: a, yf3 u1:x3xkgrzyuk6 pk8ke3z7kge 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtualkxy: zz 3kpge768k3ks: 1u3, yrfu akx?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-len 52l*nzkkz)bigth lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a convealjx 7(9sm 4eurging lens with focal length 24 cm to view a stamp 18 cm in front of the l49lx mju 7aes(ens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object y9vea1mgw;7o 4.0 mm high. What are the position, type, and height of the image? e 7my;wavgo91
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a cames+nh e:xuwl ,0ra. The maximum distance allowed betw:lx ,wnh use+0een the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify readingsf 3ztdut 8(.wr4bbcq (+2hak material by a factor of 2.5× when a book is placed 8.0 cm behind a lens. a (zct8w(b4bs3+qhtru d .fk2
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1olql))dvo5on86 p 7nn+vab 6z1peza3.5 m from an 8.0-D lens. By how much does the image move if the objectn 8np)3zv zl1bal veoop+ 57aq)66odn is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an objs 17oy1mu(cccect be placed to produce a r7u o(cc11mysceal image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be plc i2//3f pxyxlaced if its image is /fx 3xy/i p2clto be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.2+ewfak c-efyq 4 7ul60-mm-focal-length lens must an object be placed if its image is to be magnified 2.00× and be real? -lw4k2y fc7qee6+ufa   mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is xdd h .tfmc+l20cl.*x5 f o*wi1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and wh*xllc25x+ di h.0mwfco*.f td at type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an)98hv*vwof q h image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object and is real9o)w*hqv h8fv?    m

  A bright object and a viewing screen are separated by a distance*z/fktvq 6bc(xla h9- of 66.0 cm. At what location(s) between the vhb*-x9z t6/ qk(clfaobject and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length conv8z3x5gc 1qssncf+fu 4 6cuy8 ;tnehiaz+ s8a:erging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final imn ;+fut+ isasq h8fcg:ccuza53x4s 1e8z68ny age formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with p sl-cz h6dj-;;n6brc $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 c* m4w.w4 buxsim behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagr 4w.imu x*4swbam.]    cm

  The two converging lenses of Example 23g d) j1.rakxls *xn8b9–12 are now placed only 20.0 cm apart. The og)8r9j x abl nsxkd*.1bject is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of t8cgp( -ag 5sobhe lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-fogc8-ogps (b 5acal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is pl bka2o;.7 qmmaaced 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the lefta;m m27ab. qko of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 bv-* +if8fsutsfb,n 2 cm and one diverging with focal length are placed 25.0 cm apart. An object is placedtf82+ sf*vbi sfu-nb, 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a conver3r. hwnvs 71 /,voce(korf to+ging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm. What i pi* 8pugely,5s the focal length if n = 1.*p ely8pui,5 g52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the b)qt65+.a3keducd k cfocal length is 28.9 cm, what is the index of refraction of the lens matekaqu3c)bt.d+ edk6c 5rial?    cm

  A planoconcave lens (n=1.50) has a focal lengxyznc 3nrt w48k+lkwtuxt40, - t+e,eth of -23.4cm. What is the radius of the crc ku,xnektt-w+ z 8e l3+nx,yt04w4toncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has 9-,c9g xav cvx sg:gx,one flat surface and the other has R = -18.4 cm. What is the9v g gsxa-,g:cx9cx, v focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made frby6xbpj7q7 44 msxf1iom glass wit 6x7jmp44sbyq 1f7x ibh an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmakemuqph+ci b )/- xt8qz+r grinds the lens from a “+i q+-m/thz8p )uxcb qblank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each of;-vgq ( n0d6sxpz/x dther 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one ofq;nsx 0gdzf6p-(/vdx these mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming9u ; duh+we q15kufx1u pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of t+uhu1;xf9d kwu5q 1 euhe pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plastw*tab r+a*s qaz.t73 ,xefk+cic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be consideredf ur g.kzj411y a limiting case of a spherical mirror. Specify what this liz1 rjg4kfu .y1mit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrorsi-* /s fkkxq/w so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a re;ebytie/mxe el*8 9 5aal image of a real object. Can you describe a situation in which a diverging lens can form a realy;5a l/8mixb9eeee*t image?

  Each student in a physics lab is assigu8 e +drkw-x/pn ar8 2fjha0d.ned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object d a fk+x8rdhj-/.pad r80e2wnuistance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of aqx8w5l(6b z5s4 3 a a/adxxeo0qctpx: prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylinugridc.k +mu;j4(*,ph kfbz +drical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cml+d4y1 cw)ec,.ax lpp in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal length f, anvn/13m lrm1b -5gn jfbd a white scre/r3 nfl b5 nm1g1-mvjben for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose image is pf2i8bp cqm q9al )q:/erojected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If thi p)m q2/qe:c8ablf9 qe slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to b/iz) lme( 7uube projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-lenuub/)lm7(z ie gth lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real and in /b0asnvzcc2 -p 5/j(v czbg.uverted if the object is beyond the focal p0/ b5ug 2v(z-vcac jzn /.pbcsoint $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shootin 17zd3oa7cezff .0 xzjg pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as 3x7ez.f0f71 jd zzoacevidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camera wuxhoet9ed; ) -ith
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certa w**8dyg8( 1poli gxit29 kylp, b*vruin lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtual?w ,xk *8 oudrg(*p8gl* p9v1 t2biyliy    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0xf ep2vkvks8vdp+3o)q+7h.; c j al.m cm from a certain converging lens, it forms a real image.velqj3 x.+)v k72dva.8hs fpc+kp ;mo When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm